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Title: On the anisotropic advection-diffusion equation with time dependent coefficients

Abstract

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media

Authors:
 [1];  [2];  [3]
  1. UNAM (Mexico)
  2. Instituto Mexicano de Petroleo (Mexico)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1333060
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Revista Mexicana de Fisica
Additional Journal Information:
Journal Volume: 63; Journal Issue: 1; Journal ID: ISSN 0035-001X
Publisher:
Sociedad Mexicana de Physica
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; time-dependent diffusion; anisotropic media; tracer and pollutant transport

Citation Formats

Hernandez-Coronado, Hector, Coronado, Manuel, and Del-Castillo-Negrete, Diego B. On the anisotropic advection-diffusion equation with time dependent coefficients. United States: N. p., 2017. Web.
Hernandez-Coronado, Hector, Coronado, Manuel, & Del-Castillo-Negrete, Diego B. On the anisotropic advection-diffusion equation with time dependent coefficients. United States.
Hernandez-Coronado, Hector, Coronado, Manuel, and Del-Castillo-Negrete, Diego B. 2017. "On the anisotropic advection-diffusion equation with time dependent coefficients". United States. https://www.osti.gov/servlets/purl/1333060.
@article{osti_1333060,
title = {On the anisotropic advection-diffusion equation with time dependent coefficients},
author = {Hernandez-Coronado, Hector and Coronado, Manuel and Del-Castillo-Negrete, Diego B.},
abstractNote = {The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media},
doi = {},
url = {https://www.osti.gov/biblio/1333060}, journal = {Revista Mexicana de Fisica},
issn = {0035-001X},
number = 1,
volume = 63,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}

Journal Article:
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